%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN918+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:18:19 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 2 unt; 6 def)
% Number of atoms : 192 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 235 ( 88 ~; 89 |; 38 &)
% ( 6 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 60 ( 53 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ( ! [Z] :
( f(Z)
=> h(Z) )
| ! [W] :
( f(W)
=> g(W) ) )
& ! [X] :
( ( ( g(X)
& f(X) )
=> h(X) )
=> ? [Y] :
( ~ g(Y)
& f(Y) ) ) )
=> ( ! [R] :
( ( h(R)
& f(R) )
=> g(R) )
=> ? [V] :
( ~ h(V)
& g(V)
& f(V) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| ( ~ h(X)
& g(X)
& f(X) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( ~ h(X)
& g(X)
& f(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ! [X] :
( ? [Y] :
( ~ g(Y)
& f(Y) )
| sP0_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ? [Y] :
( ~ g(Y)
& f(Y) )
| ! [X] : sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( ! [V] :
( h(V)
| ~ g(V)
| ~ f(V) )
& ! [R] :
( g(R)
| ~ h(R)
| ~ f(R) )
& ( ! [Z] :
( h(Z)
| ~ f(Z) )
| ! [W] :
( g(W)
| ~ f(W) ) )
& ( ( ~ g(sK0_skl)
& f(sK0_skl) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl)],[f6]) ).
fof(f8,plain,
! [X0] :
( f(sK0_skl)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0] :
( ~ g(sK0_skl)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( h(X1)
| ~ f(X1)
| g(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( g(X0)
| ~ h(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X0] :
( h(X0)
| ~ g(X0)
| ~ f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f13,plain,
! [X] :
( ( h(X)
| ~ g(X)
| ~ f(X)
| sP0_prd(X) )
& ( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
( ! [X] :
( h(X)
| ~ g(X)
| ~ f(X)
| sP0_prd(X) )
& ! [X] :
( ( ~ h(X)
& g(X)
& f(X) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0] :
( f(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0] :
( g(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0] :
( ~ h(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,definition,
( sQ1_spl
<=> f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( ~ sQ1_spl
| f(sK0_skl) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f19,f22]) ).
fof(f26,definition,
( sQ2_spl
<=> g(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( sQ2_spl
| ~ g(sK0_skl) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f19,f26]) ).
fof(f30,definition,
! [X0] :
( sQ3_spl
<=> ( g(X0)
| ~ f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ3_spl
| g(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,definition,
! [X1] :
( sQ4_spl
<=> ( h(X1)
| ~ f(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f34,plain,
! [X0] :
( ~ sQ4_spl
| h(X0)
| ~ f(X0) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f10,f30,f33]) ).
fof(f37,plain,
! [X0] :
( ~ sQ0_spl
| f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15,f20]) ).
fof(f38,plain,
! [X0] :
( ~ sQ0_spl
| g(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f16,f20]) ).
fof(f39,plain,
! [X0] :
( ~ sQ0_spl
| ~ h(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f20]) ).
fof(f40,plain,
! [X0] :
( ~ sQ0_spl
| h(X0)
| ~ g(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f12,f37]) ).
fof(f41,plain,
! [X0] :
( ~ sQ0_spl
| ~ g(X0) ),
inference(resolution,[status(thm)],[f40,f39]) ).
fof(f42,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f38]) ).
fof(f43,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f42]) ).
fof(f44,plain,
( sQ2_spl
| ~ sQ3_spl
| ~ f(sK0_skl) ),
inference(resolution,[status(thm)],[f31,f28]) ).
fof(f45,plain,
( sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f23]) ).
fof(f46,plain,
( sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] :
( ~ sQ4_spl
| g(X0)
| ~ f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f11,f34]) ).
fof(f48,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ f(sK0_skl) ),
inference(resolution,[status(thm)],[f47,f28]) ).
fof(f49,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f23]) ).
fof(f50,plain,
( sQ2_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f49]) ).
fof(f51,plain,
$false,
inference(sat_refutation,[status(thm)],[f25,f29,f36,f43,f46,f50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN918+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 11:29:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.043184 seconds
% 0.13/0.40 % CPU time: 0.112756 seconds
% 0.13/0.40 % Total memory used: 16.634 MB
% 0.13/0.40 % Net memory used: 16.126 MB
%------------------------------------------------------------------------------